1. Field of the Invention
This invention relates generally to the field of optical microlithography, and more particularly to the simulation of a wavefront and the incorporation of a phase map to analytically account for flare in optical proximity correction of photolithographic masks.
2. Description of Related Art
The optical microlithography also known as the photolithography process in semiconductor fabrication consists of duplicating desired circuit patterns as best as possible onto a semiconductor wafer. The desired circuit patterns are typically represented as opaque and transparent regions on a template commonly called a photomask. In optical microlithography, patterns on the photomask template are projected onto photoresist-coated wafers by way of optical imaging through an exposure system.
Aerial image simulators, which compute the images generated by optical projection systems, have proven to be a valuable tool to analyze and improve the state-of-the-art in optical lithography for integrated circuit fabrication. These simulations have found application in advanced mask design, such as phase shifting mask (PSM) design, optical proximity correction (OPC), and in the design of projection optics. Modeling aerial images is a crucial component of semiconductor manufacturing. Since present lithographic tools employ partially coherent illumination, such modeling is computationally intensive for all but elementary patterns. The aerial image produced by the mask, i.e., the light intensity in an optical projection system's image plane, is a critically important quantity in microlithography for governing how well a developed photoresist structure replicates a mask design.
Optical proximity correction simulation kernels associated with lithographic processes for semiconductor chip manufacturing currently do not take into account the higher order aberrations, whose results may be realized in long-range effects, although not as prominent in the close-range of 1 to 2 micrometers. As the state of the art moves towards smaller wavelengths of light, such as 193 nm and 157 nm and extreme ultraviolet (EUV) 13 nm; and with device dimensions becoming considerably smaller in ratio to the wavelength of light that is used to print them on the wafer, the long-range effects, such as flare, become significant, making it imperative that higher order aberrations be considered.
In the prior art, data analyses have been hampered by the lack of a flare-capable simulator for handling large areas of a mask. Flare is generally defined as unwanted light in a lithographic process located in places where it should otherwise be dark. The cause of this is threefold. First, wavefront roughness or high order wavefront aberrations, which encompass up to approximately 1010 Zernikes, cause flare. Optics polishing limitations, contamination, and index variations, such as frozen turbulence inside fused silica, all contribute to wavefront roughness. Second, ghost images or stray reflections, on the order of 1% for a 99% antireflective coating, will also contribute to flare. Last, the scattering from the walls of projection optics may cause flare.
If the flare were constant, a dose shift would compensate for its effects completely. However, it is not constant, and a 1% flare variation may result in an unacceptable Across Chip Line-width Variation (ACLV). ACLV is a key parameter used to describe the fidelity of the printing process. In a design line-width of 45 nm, ACLV of 6 nm represents about +/−15% variation. The acceptable variation is nominally +/−10% or less. This large variation can considerably diminish the circuit performance and in some cases may cause a catastrophic failure. Thus, it is necessary to determine and compensate for the flare's contribution to the ACLV.
Mathematically, flare represents the sum of all halo contributions from the bright regions of the mask; the light surrounding the optical system point spread function (PSF) that is caused by scatter from within the optical system. Thus, flare scales with the bright area. In the short range, which is estimated to be on the order of Rmin˜5λ(2NA) out to 2.5 micrometers (where NA is the numerical aperture of the optical system and λ represents the wave length of the light) partial coherent effects are realized. Flare contributions add up incoherently in the medium range (2.5 to 5 micrometers) and in the long range (5 micrometers up to Rmax˜10 mm).
Other long-range effects include non-optical effects such as etch, macro loading effects, and chemical flare.
Flare increases with the area of brightness. Thus, bright field masks, where the background is clear or bright, are susceptible to flare in general. Double exposure, where two exposures with two different masks are used to print a single set of shapes, may also cause more of a flare problem. Light effectively leaks from the shield during the second exposure, adding new flare to that already produced in the primary exposure. Masks with varying pattern densities are more susceptible to flare variation. Under certain physical conditions, flare scales as the inverse square of the wavelength, 1/λ2, and can become more problematic in smaller wavelengths of light including EUV.
Experiments have demonstrated complex flare effects at multiple scales. For example, kernel anisotropy, field variations, and chemical flare have all been shown. Until now, however, data analysis has been hampered by the absence of a flare-capable simulator.
In U.S. Pat. No. 6,263,299 issued to Aleshin, et al., on Jul. 17, 2001, entitled, “GEOMETRIC AERIAL IMAGE SIMULATION,” an aerial image produced by a mask having transmissive portions was simulated by dividing the transmissive portions of the mask into primitive elements, obtaining a response for each of the primitive elements, and then simulating the aerial image by combining the responses over all of the primitive elements. However, this analytical approach does not teach or suggest a method to account for the higher order aberrations of flare within an optical proximity correction simulation kernel.
In prior art, the shape of the wavefront is represented by a series whose terms are orthogonal. The most commonly used terms are the Zernike polynomials. To date, higher order aberration effects have not been analytically expressed as polynomials in the art, in contrast to the expression of Zernike polynomials for lower order terms. In the current state of the art Optical Proximity Correction (OPC) tools, the number of Zernike polynomials used is limited up to on the order of 37. Consequently, there exists a need in the art to provide a method of accommodating the higher order aberration effects in subsequent model calibrations.
Accommodating higher order aberrations will ultimately allow for: accuracy in the computation of calibrated optical and resist models; fidelity in the wafer shapes to the “as intended” shapes by achieving better correction of mask shapes; accuracy in simulation of wafer shapes for a better understanding and evaluation of correction methodologies; increases in yield in chip manufacturing due to the better accuracy; and reduced cost in fabrication.